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   "execution_count": 1,
   "metadata": {
    "tags": [
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   "source": [
    "import sys\n",
    "import os\n",
    "if not any(path.endswith('textbook') for path in sys.path):\n",
    "    sys.path.append(os.path.abspath('../../..'))\n",
    "from textbook_utils import *                                                                                                                                                                                                                                           "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true,
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [],
   "source": [
    "heat_df = pd.read_csv('data/utilities.csv', usecols = ['temp','ccf'])\n",
    "\n",
    "heat_df = heat_df.loc[~(((heat_df['temp'] == 60) & (heat_df['ccf']==129)) | \n",
    "                        ((heat_df['temp'] == 41) & (heat_df['ccf']==16))), :]\n",
    "\n",
    "y = heat_df['ccf']\n",
    "X = heat_df[['temp']]\n",
    "\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "X1rLzRsW37jc"
   },
   "source": [
    "# Train-Test Split\n",
    "\n",
    "Although we want to use all of our data in building a model, we also want to get a sense of how\n",
    "the model behaves with new data. We often do not have the luxury of collecting additional data to assess a model, so instead we set aside a portion of our data, called the *test set*, to stand in for new data. The remainder of the data is called the *train set*, and we use this portion to build the model. Then, after we have chosen a model, we pull out the test set and see how well the model (fitted on the train set) predicts the outcomes in the test set. {numref}`Figure %s <train-test-diagram>` demonstrates this idea. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{figure} figures/TrainTestDiagram.png\n",
    "---\n",
    "name: train-test-diagram\n",
    "---\n",
    "\n",
    "The train-test split divides the data into two parts: the train set is used to build the model and the test set evaluates that model \n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Typically, the test set consists of 10\\% to 25\\% of the data.  What might not be clear from the diagram is that this division into two parts is often made at random, so the train and test sets are similar to each other. \n",
    "\n",
    "We can describe this process using the notion introduced in {numref}`Chapter %s <ch:linear>`. \n",
    "The design matrix, $ \\textbf{X} $, and outcome, $ \\mathbf{y} $, are each divided into two parts; the  design matrix, labeled $ \\textbf{X}_T $, and corresponding outcomes, $ \\mathbf{y}_T $, form the train set. We minimize the average squared loss over $\\boldsymbol{\\theta}$ with these data:  \n",
    "\n",
    "$$\n",
    "\\min_{\\boldsymbol{\\theta}} \\lVert \\mathbf{y}_T - {\\textbf{X}_T}{\\boldsymbol{{\\theta}}} \\rVert^2\n",
    "$$\n",
    "\n",
    "The coefficient, $\\boldsymbol{\\hat{\\theta}}_T$, that minimizes the training error is used to predict outcomes for the test set, which is labeled $ \\textbf{X}_S $ and $ \\mathbf{y}_S $: \n",
    "\n",
    "$$\n",
    "\\lVert \\mathbf{y}_S - {\\textbf{X}_S}{\\boldsymbol{\\hat{\\theta}}_T} \\rVert^2\n",
    "$$\n",
    "\n",
    "Since  $ \\textbf{X}_S $ and $ \\mathbf{y}_S $ are not used to build the model, they give a reasonable estimate of the loss we might expect for a new observation. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We demonstrate the train-test split with our polynomial model for gas consumption from the previous section.\n",
    "To do this, we carry out the following steps:\n",
    "\n",
    "1. Split the data at random into two parts, the train and test sets.\n",
    "2. Fit several polynomial models to the train set and choose one.\n",
    "3. Compute the MSE on the test set for the chosen polynomial (with coefficients fitted on the train set). \n",
    "\n",
    "For the first step, we divide the data with the `train_test_split` method in `scikit-learn` and set aside 22 observations for model evaluation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training set size: 75\n",
      "Test set size: 22\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "test_size = 22\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(\n",
    "    X, y, test_size=test_size, random_state=42)\n",
    "\n",
    "\n",
    "print(f'Training set size: {len(X_train)}')\n",
    "print(f'Test set size: {len(X_test)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As in the previous section, we fit models of gas consumption to various polynomials in temperature. But this time, we use only the training data: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "poly = PolynomialFeatures(degree=12, include_bias=False)\n",
    "poly_train = poly.fit_transform(X_train)\n",
    "\n",
    "degree = np.arange(1,13)\n",
    "\n",
    "mods = [LinearRegression().fit(poly_train[:, :j], y_train)\n",
    "        for j in degree]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We find the MSE for each of these models:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_squared_error\n",
    "\n",
    "error_train = [\n",
    "    mean_squared_error(y_train, mods[j].predict(poly_train[:, : (j + 1)]))\n",
    "    for j in range(12)\n",
    "]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To visualize the change in MSE, we plot MSE for each fitted polynomial against its degree:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
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    "Notice that the training error decreases with the additional model complexity.\n",
    "We saw earlier that the higher-order polynomials showed a wiggly behavior that\n",
    "we don't think reflects the underlying structure in the data. With this in\n",
    "mind, we might choose a model that is simpler but shows a large reduction in\n",
    "MSE. That could be degree 3, 4, or 5. Let's go with degree 3 since the\n",
    "difference between these three models in terms of MSE is quite small and it's\n",
    "the simplest. "
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    "Now that we have chosen our model, we provide an independent assessment of its MSE using the test set. We prepare the design matrix for the test set and use the degree 3 polynomial fitted on the train set to predict the outcome for each row in the test set. Lastly, we compute the MSE for the test set:"
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    "poly_test = poly.fit_transform(X_test)\n",
    "y_hat = mods[2].predict(poly_test[:, :3])\n",
    "\n",
    "mean_squared_error(y_test, y_hat)"
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    "The MSE for this model is quite a bit larger than the MSE computed on the training data. \n",
    "This demonstrates the problem with using the same data to fit and evaluate a model: the MSE doesn't adequately reflect the MSE for a new observation. To further demonstrate the problem with overfitting, we compute the error for the test for each of these models: "
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   "execution_count": 8,
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    "error_test = [\n",
    "    mean_squared_error(y_test, mods[j].predict(poly_test[:, : (j + 1)]))\n",
    "    for j in range(12)\n",
    "]"
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    "In practice, we do not look at the test set until we have committed to a model. Alternating between fitting a model on the train set and evaluating it on the test set can lead to overfitting. But for demonstration purposes, we plot the MSE on the test set for all of the polynomial models we fitted: "
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "degree = np.arange(1, 13)\n",
    "\n",
    "fig = go.Figure()\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter(\n",
    "        x=degree,\n",
    "        y=error_test,\n",
    "        line=dict(color=\"DarkOrange\", width=2, dash=\"dot\"),\n",
    "    )\n",
    ")\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter(\n",
    "        x=degree,\n",
    "        y=error_train,\n",
    "        line=dict(color=\"MediumBlue\", width=2, dash=\"dash\"),\n",
    "    )\n",
    ")\n",
    "\n",
    "fig.add_annotation(x=3, y=450, showarrow=False, text=\"Test set MSE\")\n",
    "\n",
    "fig.add_annotation(x=7, y=175, showarrow=False, text=\"Train set MSE\")\n",
    "\n",
    "fig.update_layout(\n",
    "    showlegend=False,\n",
    "    width=350,\n",
    "    height=250,\n",
    "    xaxis_title=\"Degree of polynomial\",\n",
    "    yaxis_title=\"MSE\",\n",
    ")\n",
    "\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice how the MSE for the test set is larger than the MSE for the train set for all models, not just the model that we selected.  More importantly, notice how the MSE for the test set initially decreases as the model goes from underfitting to one that follows the curvature in the data a bit better. Then, as the model grows in complexity, the MSE for the test set increases. These more complex models overfit the training data and lead to large errors in predicting the test set. An idealization of this phenomenon is captured in the diagram in {numref}`Figure %s <train-test-overfit>`.    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{figure} figures/train-test-overfitting.png\n",
    "---\n",
    "name: train-test-overfit\n",
    "width: 350px\n",
    "---\n",
    "\n",
    "As the model grows in complexity, the train set error shrinks and the test set error increases\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The test data provides an assessment of the prediction error for new observations.  It is crucial to use the test set only once, after we have committed to a model. Otherwise, we fall into the trap of using the same data to choose and evaluate the model. When choosing the model, we fell back on the simplicity argument because we were aware that increasingly complex models tend to overfit. However, we can extend the train-test method to help select the model as well. This is the topic of the next section. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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